applied sciences Article Design and Implementation of Ternary Logic Integrated Circuits by Using Novel Two-Dimensional Materials Mingqiang Huang 1, Xingli Wang 1, Guangchao Zhao 1, Philippe Coquet 1,2 and Bengkang Tay 1,* 1 CNRS-International-NTU-THALES-Research-Alliance (CINTRA), Nanyang Technological University, Singapore 639798, Singapore; [email protected] (M.H.); [email protected] (X.W.); [email protected] (G.Z.); [email protected] (P.C.) 2 Institut d’Electronique, de Microélectronique et de Nanotechnologie (IEMN), CNRS UMR 8520-Université de Lille, 59650 Villeneuve d’Ascq, France * Correspondence: [email protected]; Tel.: +65-6790-4533 Received: 29 August 2019; Accepted: 4 October 2019; Published: 9 October 2019 Abstract: With the approaching end of Moore’s Law (that the number of transistors in a dense integrated circuit doubles every two years), the logic data density in modern binary digital integrated circuits can hardly be further improved due to the physical limitation. In this aspect, ternary logic (0, 1, 2) is a promising substitute to binary (0, 1) because of its higher number of logic states. In this work, we carry out a systematical study on the emerging two-dimensional (2D) materials (MoS2 and Black Phosphorus)-based ternary logic from individual ternary logic devices to large scale ternary integrated circuits. Various ternary logic devices, including the standard ternary inverter (STI), negative ternary inverter (NTI), positive ternary inverter (PTI) and especially the ternary decrement cycling inverter (DCI), have been successfully implemented using the 2D materials. Then, by taking advantage of the optimized ternary adder algorithm and the novel ternary cycling inverter, we design a novel ternary ripple-carry adder with great circuitry simplicity. Our design shows about a 50% reduction in the required number of transistors compared to the existing ternary technology. This work paves a new way for the ternary integrated circuits design, and shows potential to fulfill higher logic data density and a smaller chip area in the future. Keywords: 2D materials; black phosphorus; inverter; ternary logic; adder 1. Introduction Integrated circuits (IC) are the cornerstone of modern information society and are widely used in almost all of the electronic systems. Binary digital integrated circuits are the most prevalent computing technology today, because the binary signals exist naturally in semiconductor electronic devices, and binary Boolean Algebra can be easily implemented by using binary logic gates. However, the performance of binary logic is fundamentally limited by its low density of logic states, that is, only two logic levels (0, 1) can be transmitted over a given set of lines [1]. Therefore, it needs a large number of logic gates and transistors to reach the required data size. Besides, even more interconnected wirings between the system components are required in integrated circuits. For example, in a very large scale integrated (VLSI) circuit, approximately 70 percent of the area is devoted to interconnection, 20 percent to insulation, and only 10 percent to device [1–3], which exceedingly increases the complexity, both in design and manufacture. A ternary digit, which is also called as a trit, owns three significant values (0, 1, 2), and can represent log2(3) = 1.58 bits [4–6]. Thus, more information can be transmitted over the interconnections, Appl. Sci. 2019, 9, 4212; doi:10.3390/app9204212 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 4212 2 of 13 and less devices are required for a given data length. For instance, a ternary system with a digit size = 19 can represent a data size about 319~1 G. Meanwhile, that of a binary system is only 219~0.5 M. Ternary logic has been widely studied for decades, but is still severely blocked by the fact that the designs of ternary are much more complex than those of binary. In the 1980s, the design of silicon CMOS ternary occurred as a moderate breakthrough, where one p-MOSFET, two resistors and one n-MOSFET were in-series connected [4,5]. Such circuits simplified the design, but it required two passive resistive resistors, and increased the production complexity. More seriously, it largely increased the static power consumption because of the two resistors with relative low resistance. In the 1990s, the carbon nanotube field effect transistor (CNTFET) showed itself to be promising for its ballistic transport, high mobility and low off-current properties [7,8]. And it was then found that the threshold voltage of CNTFET could be well determined by its diameter, which was quite suitable for the ternary threshold logic design [9,10]. Based upon that, many groups have focused their attention on the demonstration of ternary logic gates using multi-threshold CNTFETs [11–15]. In their designs, no passive resistive components were needed, but the simplest ternary NOT gate still needed six CNTFETs, which was much more complicated than that of a classical CMOS binary NOT gate (two FETs). Therefore, both the silicon ternary and CNT ternary are not cost-efficient enough to establish a practical ternary application: It needs four transistors in silicon ternary and six transistors in CNT ternary to process one trit (which equals 1.58 bits) of information. Meanwhile, one can use the same four (or six) transistors to process two (or three) bits of information in binary logic circuits. A recent breakthrough on ternary logic is the demonstration of a ternary NOT gate by using the commercial CMOS processes [16]. But it suffers from the low operation frequency due to the ultra-low current, and the other types of ternary logic functions are still undiscovered. Recently, the emerging two-dimensional (2D) semiconducting materials, such as graphene, transitional metal dichalcogenides (TMDs) and black phosphorus (BP), have attracted enormous attention due to their excellent electronic properties [17–23], and this also opens up new possibilities in logic circuits in terms of both CMOS binary [24,25] and ternary logic design [26–31]. For example, Tomas Palacios et al. [26] presented the first 2D-materials-based standard ternary inverter in 2016. Huang et al. [28] designed and fabricated the novel tunable MoS2/BP-based ternary devices (tuned by the electric field and device channel length). Jin-Hong Park et al. [29] demonstrated the graphene/WSe2-based light triggered ternary device. However, all of these previous works are mainly focused on the demonstration of a standard ternary inverter (STI). To accomplish simplicity in circuit design and increase the data density in practical integrated circuits, further research on ternary logic devices, circuits and algorithms needs to be explored. In this work, we propose to perform a systematical study on the 2D-based ternary logic from individual ternary logic gates to large scale ternary integrated circuits. We will firstly utilize the unique electronic properties of ambipolar BP transistors and N-type MoS2 transistors to build various ternary logic gates. Then we will integrate the as-demonstrated logic gates to design and realize the dyadic ternary operators such as T-NAND, T-NOR and other ternary functions. Finally, we will focus on the design of large scale ternary integrated circuits applications. The decrement cycling inverter and the optimized ternary adder algorithm will be used to design the 19-trit ternary adder. 2. Demonstration of Ternary Logic Gates In conventional binary Boolean Logic, there are a total of 22 = 4 monadic functions. While in ternary logic [6], the number of monadic functions is 33 = 27. These 27 ternary functions are enumerated from 0 to 9 and then A to Z, as shown in Figure1a. Strictly speaking, we do not need all of these functions because there are strong relationships between such operations in Boolean Algebra. Several of them are nontrivial and meaningful [6]. For example, functions 0, D, and Z are the trivial, constant-valued functions; Function P is identity; Function 5 is the standard ternary inverter (STI); Functions 2 and 8 are the negative threshold inverter (NTI) and positive threshold inverter (PTI), respectively; Functions 7 and B are increment cycling inverter (ICI) and decrement cycling inverter Appl. Sci. 2019, 9, 4212 3 of 13 Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 13 (DCI), respectively. It is widely accepted that the most important and fundamental components in ternaryternary logiclogic areare STI,STI, NTINTI andand PTI PTI [ 9[9–12].–12]. TheThe output-inputoutput-input characteristiccharacteristic curvescurves ofof suchsuch ternaryternary functionsfunctions have have been been shown shown in in Figure Figure1 b.1b. STISTI isis actuallyactually aa ternaryternary NOTNOT functionfunction thatthat invertsinverts itsits input,input, returningreturning “0”“0” whenwhen givengiven “2”“2” andand vicevice versa,versa, whilewhile leavingleaving “1”“1” inputsinputs unchanged;unchanged; NTINTI invertsinverts thethe inputinput ofof “2”“2” andand “0”“0” asas samesame asas thethe NOTNOT function,function, butbut returnsreturns “0”“0” whenwhen givengiven “0”;“0”; PTIPTI invertsinverts thethe inputinput ofof “2”“2” andand “0”,“0”, butbut returnsreturns “2”“2” whenwhen givengiven “1”.“1”. CyclingCycling ternaryternary (CT)(CT) gatesgates cancan operate operate the the increment increment function function (output (output= =input input+ + 1)1) oror decrementdecrement functionfunction (output(output= = inputinput -- 1),1), whichwhich areare especiallyespecially suitablesuitable forfor thethe ternaryternary